With unsigned binary representation, what is the range of numbers as written in binary
and in decimal for the following cells?

(e)an n-bit cell in general

This problem comes from the Computer Systems by Warford book if that helps. I don't know how to write it. I know for example a three bit cell the answer is:
in binary 000-111 and decimal 0 to 7.

Feb 2nd 2014, 01:09 PM

romsek

Re: The range of numbers of an n-bit cell in general?

Quote:

Originally Posted by lamentofking

With unsigned binary representation, what is the range of numbers as written in binary
and in decimal for the following cells?

(e)an n-bit cell in general

This problem comes from the Computer Systems by Warford book if that helps. I don't know how to write it. I know for example a three bit cell the answer is:
in binary 000-111 and decimal 0 to 7.

in general, in base k, n digits can represent kn numbers so if 0 is to be your first number you have the range of [0,kn-1].

for binary k=2
for decimal k=10

Feb 5th 2014, 10:39 AM

lamentofking

Re: The range of numbers of an n-bit cell in general?

Quote:

Originally Posted by romsek

in general, in base k, n digits can represent kn numbers so if 0 is to be your first number you have the range of [0,kn-1].

for binary k=2
for decimal k=10

And for two's complement binary representation, with a 7-bit cell, would the range be [-7,6]? I'm guessing the formula could be [-n, to n-1], where n is the number of bits in the cell. but that's decimal . I don't know how to write it for binary.

Feb 5th 2014, 11:41 AM

romsek

Re: The range of numbers of an n-bit cell in general?

Quote:

Originally Posted by lamentofking

And for two's complement binary representation, with a 7-bit cell, would the range be [-7,6]? I'm guessing the formula could be [-n, to n-1], where n is the number of bits in the cell. but that's decimal . I don't know how to write it for binary.